Large N Partition Functions, Holography, and Black Holes.

We present a simple closed form expression for the topologically twisted index of the ABJM theory as a function of the magnetic fluxes and complex chemical potentials valid at fixed k and to all orders in the 1/N expansion. This in turn leads to analytic expressions for the topologically twisted index at fixed genus in the 't Hooft limit to all orders in the 1/sqrt[λ] expansion. These results have important implications for holography and the microscopic entropy counting of supersymmetric static AdS_{4} black holes.

Unreasonable Effectiveness of Higher Derivative Supergravity in AdS_{4} Holography.

We study four-derivative corrections to four-dimensional N=2 minimal gauged supergravity controlled by two real constants. The solutions of the equations of motion in the two-derivative theory are not modified by the higher-derivative corrections. We use this to derive a general formula for the regularized on-shell action for any asymptotically locally AdS_{4} solution of the theory and show how the higher-derivative corrections affect black hole thermodynamic quantities in a universal way.